ToothGrowth
## len supp dose
## 1 4.2 VC 0.5
## 2 11.5 VC 0.5
## 3 7.3 VC 0.5
## 4 5.8 VC 0.5
## 5 6.4 VC 0.5
## 6 10.0 VC 0.5
## 7 11.2 VC 0.5
## 8 11.2 VC 0.5
## 9 5.2 VC 0.5
## 10 7.0 VC 0.5
## 11 16.5 VC 1.0
## 12 16.5 VC 1.0
## 13 15.2 VC 1.0
## 14 17.3 VC 1.0
## 15 22.5 VC 1.0
## 16 17.3 VC 1.0
## 17 13.6 VC 1.0
## 18 14.5 VC 1.0
## 19 18.8 VC 1.0
## 20 15.5 VC 1.0
## 21 23.6 VC 2.0
## 22 18.5 VC 2.0
## 23 33.9 VC 2.0
## 24 25.5 VC 2.0
## 25 26.4 VC 2.0
## 26 32.5 VC 2.0
## 27 26.7 VC 2.0
## 28 21.5 VC 2.0
## 29 23.3 VC 2.0
## 30 29.5 VC 2.0
## 31 15.2 OJ 0.5
## 32 21.5 OJ 0.5
## 33 17.6 OJ 0.5
## 34 9.7 OJ 0.5
## 35 14.5 OJ 0.5
## 36 10.0 OJ 0.5
## 37 8.2 OJ 0.5
## 38 9.4 OJ 0.5
## 39 16.5 OJ 0.5
## 40 9.7 OJ 0.5
## 41 19.7 OJ 1.0
## 42 23.3 OJ 1.0
## 43 23.6 OJ 1.0
## 44 26.4 OJ 1.0
## 45 20.0 OJ 1.0
## 46 25.2 OJ 1.0
## 47 25.8 OJ 1.0
## 48 21.2 OJ 1.0
## 49 14.5 OJ 1.0
## 50 27.3 OJ 1.0
## 51 25.5 OJ 2.0
## 52 26.4 OJ 2.0
## 53 22.4 OJ 2.0
## 54 24.5 OJ 2.0
## 55 24.8 OJ 2.0
## 56 30.9 OJ 2.0
## 57 26.4 OJ 2.0
## 58 27.3 OJ 2.0
## 59 29.4 OJ 2.0
## 60 23.0 OJ 2.0
head(ToothGrowth)
## len supp dose
## 1 4.2 VC 0.5
## 2 11.5 VC 0.5
## 3 7.3 VC 0.5
## 4 5.8 VC 0.5
## 5 6.4 VC 0.5
## 6 10.0 VC 0.5
str(ToothGrowth)
## 'data.frame': 60 obs. of 3 variables:
## $ len : num 4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
## $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
## $ dose: num 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...
summary(ToothGrowth)
## len supp dose
## Min. : 4.20 OJ:30 Min. :0.500
## 1st Qu.:13.07 VC:30 1st Qu.:0.500
## Median :19.25 Median :1.000
## Mean :18.81 Mean :1.167
## 3rd Qu.:25.27 3rd Qu.:2.000
## Max. :33.90 Max. :2.000
library(ggplot2)
#boxplot of tooth length
ggplot(ToothGrowth, aes(y=len))+
geom_boxplot(fill = "pink") +
labs(title = "Boxplot of Tooth Length (len)")
y = "Tooth length" +
theme_minimal()
library(ggplot2)
#histogram
ggplot(ToothGrowth, aes(x= len)) +
geom_histogram(binwidth = 2, fill = "skyblue", color = "black") +
labs(title = "Histogram of Tooth Length (len)" ,
x = "Tooth Length", y = "Frequency") +
theme_minimal()
#Q3
#ho: The average tooth length is greather than or equal to 17.
#ho: The average tooth length is less than 17.
#Q4: It should be one-tailed test because we want to specifically test whether the tooth length is less than 17, not just different from 17.
#Q5: We calculate the t-value because population standard deviation is unknown.
#Q6:
data <- ToothGrowth$len
sample_mean <- mean(data)
sample_sd <- sd(data)
sample_size <- length(data)
pop_mean <- 17
alpha <- 0.05
#calculating standar error
standard_error <- sample_sd/ sqrt(sample_size)
#calculate t-statistics
t_value <- (sample_mean - pop_mean) / standard_error
print(t_value)
## [1] 1.836245
#degree of freedom
df <- sample_size -1
#calculate p-value for right tailed test
p_value <- pt(t_value, df)
print(p_value)
## [1] 0.9643194
#since the p-value is 0.96, we accept the null hypothesis.